## A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons (1991)

Citations: | 103 - 2 self |

### BibTeX

@MISC{Seidel91asimple,

author = {Raimund Seidel},

title = {A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons},

year = {1991}

}

### OpenURL

### Abstract

### Citations

295 |
Triangulating a simple polygon in linear time
- Chazelle
- 1991
(Show Context)
Citation Context ...ars later. In the mean time Clarkson et al. had published a randomized algorithm with O(n log n) expected running time [CTV]. Finally in 1990 Chazelle discovered a linear time deterministic algorithm =-=[C90]-=-, which settles the question about the intrinsic computational complexity of triangulating once and for all. This paper presents another randomized algorithm with O(n log n) expected running time. Its... |

76 |
A theorem on polygon cutting with applications
- Chazelle
- 1982
(Show Context)
Citation Context ...A brief history: Garey et al. [GJPT] were the first to publish an O(n log n) algorithm based on sweeping in 1978. Four years later another algorithm with the same complexity was published by Chazelle =-=[C82]. The O(n -=-log n) bound was then improved to bounds of the form O(n log C P ), where C P is a "shape" parameter no bigger than n that depends on the polygon P to be triangulated (for instance the numbe... |

69 |
Triangulating a simple polygon
- Garey, Johnson, et al.
- 1978
(Show Context)
Citation Context ... importance in various application areas; and finally, the actual computational complexity of the problem remained unresolved for more than a decade until very recently. A brief history: Garey et al. =-=[GJPT]-=- were the first to publish an O(n log n) algorithm based on sweeping in 1978. Four years later another algorithm with the same complexity was published by Chazelle [C82]. The O(n log n) bound was then... |

57 |
Triangulating simple polygons and equivalent problems
- Fournier, Montuno
- 1984
(Show Context)
Citation Context ... then improved to bounds of the form O(n log C P ), where C P is a "shape" parameter no bigger than n that depends on the polygon P to be triangulated (for instance the number of reflex vert=-=ices [HM],[FM], or the &-=-quot;sinuosity" of P [CI]). On a different front an ever-increasing class of polygons were shown to be triangulatable in linear time [TA82], [T88]. After a false start, Tarjan and Van Wyk [TV] ma... |

42 | Triangulation and shape-complexity
- Chazelle, Incerpi
- 1984
(Show Context)
Citation Context ...e form O(n log C P ), where C P is a "shape" parameter no bigger than n that depends on the polygon P to be triangulated (for instance the number of reflex vertices [HM],[FM], or the "s=-=inuosity" of P [CI]-=-). On a different front an ever-increasing class of polygons were shown to be triangulatable in linear time [TA82], [T88]. After a false start, Tarjan and Van Wyk [TV] made a major breakthrough with a... |

41 |
Fast triangulation of a simple polygon
- Hertel, Mehlhorn
- 1983
(Show Context)
Citation Context ...d was then improved to bounds of the form O(n log C P ), where C P is a "shape" parameter no bigger than n that depends on the polygon P to be triangulated (for instance the number of reflex=-= vertices [HM],[FM], or -=-the "sinuosity" of P [CI]). On a different front an ever-increasing class of polygons were shown to be triangulatable in linear time [TA82], [T88]. After a false start, Tarjan and Van Wyk [T... |

36 | An O(n loglog n)-time algorithm for triangulating a simple polygon
- Tarjan, Wyk
- 1988
(Show Context)
Citation Context ...M],[FM], or the "sinuosity" of P [CI]). On a different front an ever-increasing class of polygons were shown to be triangulatable in linear time [TA82], [T88]. After a false start, Tarjan an=-=d Van Wyk [TV]-=- made a major breakthrough with an O(n log log n) algorithm in 1986. This time bound was matched by a different but simpler algorithm by Kirkpatrick et al. [KKT] three years later. In the mean time Cl... |

28 |
Sorting Jordan sequences in linear time using level-linked search trees
- Hoffman, Mehlhorn, et al.
- 1986
(Show Context)
Citation Context ...l. This paper presents another randomized algorithm with O(n log n) expected running time. Its virtues lie in its simplicity. It uses no divide-and-conquer or recursion, and no "Jordan-sorting&qu=-=ot; [CTV],[HMRT]-=-. Its expected performance admits a very straightforward and self-contained analysis. Finally, it is practical and relatively simple to implement, a property that very few, if any, of the algorithms m... |

24 |
A fast Las Vegas algorithm for triangulating a simple polygon, Discrete Comput
- Clarkson, Tarjan, et al.
- 1989
(Show Context)
Citation Context ...matched by a different but simpler algorithm by Kirkpatrick et al. [KKT] three years later. In the mean time Clarkson et al. had published a randomized algorithm with O(n log n) expected running time =-=[CTV]-=-. Finally in 1990 Chazelle discovered a linear time deterministic algorithm [C90], which settles the question about the intrinsic computational complexity of triangulating once and for all. This paper... |

23 | Randomized parallel algorithms for trapezoidal diagrams
- Clarkson, Cole, et al.
- 1991
(Show Context)
Citation Context ...ed cost for this over the entire algorithm is O(log n) per component. 4 Remarks An algorithm somewhat similar to the one described in this paper has also been discovered by Clarkson, Cole, and Tarjan =-=[CCT]-=-. However, their approach is based on divide-and-conquer and the main thrust of their approach is towards a fast parallel trapezoidation algorithm. Our algorithm can be viewed as a holistic version of... |

17 |
On a convex hull algorithm for polygons and its applications to triangulation problems
- Toussaint, Avis
- 1982
(Show Context)
Citation Context ...ngulated (for instance the number of reflex vertices [HM],[FM], or the "sinuosity" of P [CI]). On a different front an ever-increasing class of polygons were shown to be triangulatable in li=-=near time [TA82]-=-, [T88]. After a false start, Tarjan and Van Wyk [TV] made a major breakthrough with an O(n log log n) algorithm in 1986. This time bound was matched by a different but simpler algorithm by Kirkpatric... |

6 |
An output-complexity-sensitive polygon triangulation algorithm
- Toussaint
- 1988
(Show Context)
Citation Context ... (for instance the number of reflex vertices [HM],[FM], or the "sinuosity" of P [CI]). On a different front an ever-increasing class of polygons were shown to be triangulatable in linear tim=-=e [TA82], [T88]-=-. After a false start, Tarjan and Van Wyk [TV] made a major breakthrough with an O(n log log n) algorithm in 1986. This time bound was matched by a different but simpler algorithm by Kirkpatrick et al... |

4 |
O(n log log n) polygon triangulation with simple data structures
- Kirkpatrick, Klawe, et al.
- 1990
(Show Context)
Citation Context ...After a false start, Tarjan and Van Wyk [TV] made a major breakthrough with an O(n log log n) algorithm in 1986. This time bound was matched by a different but simpler algorithm by Kirkpatrick et al. =-=[KKT]-=- three years later. In the mean time Clarkson et al. had published a randomized algorithm with O(n log n) expected running time [CTV]. Finally in 1990 Chazelle discovered a linear time deterministic a... |

1 | O(n log logn) polygon triangulation with simple data structures - Kirkpatrick, Klawe, et al. - 1990 |

1 | Wyk An O(n loglogn)-time algorithm for triangulating a simple polygon - Tarjan, Van - 1988 |